On the basis of thermochemical equations (a), (b) and (c), find out which of the algebric relationships given in options (i) to (iv) is correct.

(a) C (graphite) + O₂ (g) → CO₂ (g) ; ∆_rH = x kJ/ mol

(b) C (graphite) + $\frac{1}{2}$ O₂ (g) → CO (g) ; ∆_rH = y kJ/ mol

(c) CO (g) $\frac{1}{2}$ +  O2 (g) → CO₂ (g) ; ∆_rH = z kJ/ mol

(i) z = x + y

(ii) x = y – z

(iii) x = y + z

(iv) y = 2z – x